SmolLm2-Thinker

Uploaded model

• Developed by: andy-grxwthio
• License: apache-2.0
• Finetuned from model : HuggingFaceTB/SmolLM2-1.7B-Instruct

This llama model was trained 2x faster with Unsloth and Huggingface's TRL library.

<img src="https://raw.githubusercontent.com/unslothai/unsloth/main/images/unsloth%20made%20with%20love.png" width="200"/>

Before:

"Pi, or π, is a mathematical constant representing the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14159. However, it's a transcendental number, meaning it cannot be expressed as a finite decimal or fraction. Therefore, it cannot be calculated exactly using any finite number of decimal places. But you can use various mathematical formulas or algorithms to calculate it to a high degree of accuracy. For instance, you can use the following simple formula to estimate pi:\n\nPi = 4 * (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...)\n\nThis is known as the Leibniz formula for π. For more accurate calculations, you could use the Gauss-Legendre algorithm or the Chudnovsky algorithm. Please note that these calculations can be quite complex and may require significant computational resources."

After:

"<reasoning>\nPi, denoted as π, is an irrational number representing the ratio of a circle's circumference to its diameter. This ratio is constant for all circles, regardless of size. To calculate pi, we can use various methods such as the Monte Carlo method, infinite series, or infinite products.\n\nOne commonly used method is the Monte Carlo method, which involves generating random points within a square and counting how many fall within a quarter circle inscribed within the square. The ratio of points within the circle to the total number of points approximates π/4.\n\nAnother method is the infinite series expansion of pi: π = 4 * (1 - 1/3 + 1/5 - 1/7 + ...). This expansion involves an infinite sum of terms, each of which is a fraction of a decreasing odd number. The more terms we include in the sum, the more accurate our approximation of π will be.\n\nAn infinite product representation of pi is also well-known: π = 2 / (1 * 2 + 1 / (2 * 3 + 1 / (2 * 3 * 4 + ...))). This product involves an infinite sequence of terms, each of which is a fraction of the product of consecutive integers.\n\nUsing these methods, we can calculate pi to an arbitrary degree of precision.\n\n</reasoning>\n<answer>\nPi has been calculated to over 31.4 trillion digits using advanced computers and algorithms. One of the most efficient algorithms for calculating pi is the Gauss-Legendre Algorithm, which approximates the value of pi using an infinite series. This algorithm involves a series of mathematical operations that converge to the value of pi with high accuracy.\n\nFor example, the first 31 digits of pi are: 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679...\n\nPi has numerous applications in mathematics, physics, engineering, and computer science, ranging from the geometry of circles and spheres to the calculation of the volumes of solids.\n\nAdditionally, pi has many fascinating properties and appearances in mathematics, such as its connection to the Fibonacci sequence, the Riemann zeta function, and the distribution of prime numbers.\n\nIn conclusion, pi is a fundamental constant in mathematics, and its calculation has become a benchmark of computational power. Its infinite nature and irrationality make it a challenge to calculate to high precision, but the pursuit of this challenge continues to inspire mathematical innovation and discovery.\n\n</answer>"

Trained on Dolphin-R1 to allow it to start generating